DPI and Pixels

[RKissane]

Ok I know this has been covered before but I am more confused now on how Xara handles DPI and Pixels when loading a picture.

What I have is a picture that we purchased for commercial use.
The picture is specified as being 3831 x 2554 px - 12.77" x 8.51" at 300DPI

I look at this picture in Corel Painter Essentials and Gimp everything matches up what it is specified as. If I take a the original size of the picture in pixels and divide by the 30DPI it comes out to 12.77" x 8.5"

When I bring this picture into Xara and tell it to come in at the DPI specified in comes in way bigger at 39.9" x 26.9". Where does this size come from?

If I save the file at 300DPI I then get a file that says it is 11972 × 7982 pixels. Which matches up to the inch size it came in as.

If I setup Xara to open the file as 96DPI for 1:1 scaling I still get the same large size in inches. And if I save the file as 96 DPI it keeps the size in inches and says it is 96DPI when I look at the image properties in either Corel or Gimp.

What am I missing and why does Xara work differently than what other programs do in regard to DPI and pixels?

I should point out that this is for print work.

Thanks
Ray